The Projections of Convex Lattice Sets of Points in

Algorithm 1

Plane sweep algorithm.

Require:

  coordinate matrix and primitive direction .

Ensure:

  .

   . Let correspond to points .

   Initialize an empty event queue . Next, insert the point into . (Rename to

   [Remark 7] by the insert-order [Remark 6] of lattice points).

   Initialize an empty stack and an empty linked list .

   while ( is not empty) do

    Determine the next event point in and delete it.

     HANDLEEVENTPOINT

     ORIGINSYMMETRY

   end while

   Initialize an empty variable [Remark 9].

 if () then

  .

 else

  .

 end if

 Compute the value of [Remark 8], and assigned to .